Single-Peaked Consistency for Weak Orders Is Easy

It is well known that single-peaked consistency for total orders is in P. However in practice a preference profile is not always comprised of total orders. Often voters have indifference between some of the candidates. In a weak preference order indifference must be transitive. We show that single-peaked consistency for weak orders is in P for the three different variants of single-peakedness for weak orders. Specifically, we consider Black's original definition for weak orders (Black 1948), single-plateaued preferences (Black 1958), and the existential model recently introduced by Lackner (2014). We accomplish this by transforming each of these single-peaked consistency problems to the problem of determining if a 0-1 matrix has the property of consecutive ones in rows.